A comparison of approaches for simultaneous inference of fixed effects for multiple outcomes using linear mixed models

Longitudinal studies with multiple outcomes often pose challenges for the statistical analysis. A joint model including all outcomes has the advantage of incorporating the simultaneous behavior but is often difficult to fit due to computational challenges. We consider 2 alternative approaches to quantify and assess the loss in efficiency as compared with joint modelling when evaluating fixed effects. The first approach is pairwise fitting of pseudolikelihood functions for pairs of outcomes. The second approach recovers correlations between parameter estimates across multiple marginal linear mixed models. The methods are evaluated in terms of a data example both from a study on the effects of milk protein on health in young adolescents and in an extensive simulation study. We find that the 2 alternatives give similar results in settings where an exchangeability condition is met, but otherwise, pairwise fitting shows a larger loss in efficiency than the marginal models approach. Using an alternative to the joint modelling strategy will lead to some but not necessarily a large loss of efficiency for small sample sizes.     

A high-dimensional joint model for longitudinal outcomes of different nature

In repeated dose-toxicity studies, many outcomes are repeatedly measured on the same animal to study the toxicity of a compound of interest. This is only one example in which one is confronted with the analysis of many outcomes, possibly of a different type. Probably the most common situation is that of an amalgamation of continuous and categorical outcomes. A possible approach towards the joint analysis of two longitudinal outcomes of a different nature is the use of random-effects models (Models for Discrete Longitudinal Data. Springer Series in Statistics. Springer: New York, 2005). Although a random-effects model can easily be extended to jointly model many outcomes of a different nature, computational problems arise as the number of outcomes increases. To avoid maximization of the full likelihood expression, Fieuws and Verbeke (Biometrics 2006; 62:424-431) proposed a pairwise modeling strategy in which all possible pairs are modeled separately, using a mixed model, yielding several different estimates for the same parameters. These latter estimates are then combined into a single set of estimates. Also inference, based on pseudo-likelihood principles, is indirectly derived from the separate analyses. In this paper, we extend the approach of Fieuws and Verbeke (Biometrics 2006; 62:424-431) in two ways: the method is applied to different types of outcomes and the full pseudo-likelihood expression is maximized at once, leading directly to unique estimates as well as direct application of pseudo-likelihood inference. This is very appealing when interested in hypothesis testing. The method is applied to data from a repeated dose-toxicity study designed for the evaluation of the neurofunctional effects of a psychotrophic drug. The relative merits of both methods are discussed. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Incorporating patient-reported outcomes in dose-finding clinical trials

Oncology dose-finding clinical trials determine the maximum tolerated dose (MTD) based on toxicity outcomes captured by clinicians. With the availability of more rigorous instruments for measuring toxicity directly from patients, there is a growing interest to incorporate patient-reported outcomes (PRO) in clinical trials to inform patient tolerability. This is particularly important for dose-finding trials to ensure the identification of a well-tolerated dose. In this paper, we propose three extensions of the continual reassessment method (CRM), termed PRO-CRMs, that incorporate both clinician and patient outcomes. The first method is a marginal modeling approach whereby clinician and patient toxicity outcomes are modeled separately. The other two methods impose a constraint using a joint outcome defined based on both clinician and patient toxicities and model them either jointly or marginally. Simulation studies show that while all three PRO-CRMs select well-tolerated doses based on clinician's and patient's perspectives, the methods using a joint outcome perform better and have similar performance. We also show that the proposed PRO-CRMs are consistent under robust model assumptions.     

Toward Rigorous Idiographic Research in Prevention Science: Comparison Between Three Analytic Strategies for Testing Preventive Intervention in Very Small Samples

Psychosocial prevention research lacks evidence from intensive within-person lines of research to understand idiographic processes related to development and response to intervention. Such data could be used to fill gaps in the literature and expand the study design options for prevention researchers, including lower-cost yet rigorous studies (e.g., for program evaluations), pilot studies, designs to test programs for low prevalence outcomes, selective/indicated/adaptive intervention research, and understanding of differential response to programs. This study compared three competing analytic strategies designed for this type of research: autoregressive moving average, mixed model trajectory analysis, and P-technique. Illustrative time series data were from a pilot study of an intervention for nursing home residents with diabetes (N?=?4) designed to improve control of blood glucose. A within-person, intermittent baseline design was used. Intervention effects were detected using each strategy for the aggregated sample and for individual patients. The P-technique model most closely replicated observed glucose levels. ARIMA and P-technique models were most similar in terms of estimated intervention effects and modeled glucose levels. However, ARIMA and P-technique also were more sensitive to missing data, outliers and number of observations. Statistical testing suggested that results generalize both to other persons as well as to idiographic, longitudinal processes. This study demonstrated the potential contributions of idiographic research in prevention science as well as the need for simulation studies to delineate the research circumstances when each analytic approach is optimal for deriving the correct parameter estimates.     

A new modeling approach for quantifying expert opinion in the drug discovery process

Expert opinion plays an important role when choosing clusters of chemical compounds for further investigation. Often, the process by which the clusters are assigned to the experts for evaluation, the so‐called selection process, and the qualitative ratings given by the experts to the clusters (chosen/not chosen) need to be jointly modeled to avoid bias. This approach is referred to as the joint modeling approach. However, misspecifying the selection model may impact the estimation and inferences on parameters in the rating model, which are of most scientific interest. We propose to incorporate the selection process into the analysis by adding a new set of random effects to the rating model and, in this way, avoid the need to model it parametrically. This approach is referred to as the combined model approach. Through simulations, the performance of the combined and joint models was compared in terms of bias and confidence interval coverage. The estimates from the combined model were nearly unbiased, and the derived confidence intervals had coverage probability around 95% in all scenarios considered. In contrast, the estimates from the joint model were severely biased under some form of misspecification of the selection model, and fitting the model was often numerically challenging. The results show that the combined model may offer a safer alternative on which to base inferences when there are doubts about the validity of the selection model. Importantly, thanks to its greater numerical stability, the combined model may outperform the joint model even when the latter is correctly specified. Copyright © 2015 John Wiley & Sons, Ltd.     

Inference for correlated effect sizes using multiple univariate meta‐analyses

Multivariate meta‐analysis, which involves jointly analyzing multiple and correlated outcomes from separate studies, has received a great deal of attention. One reason to prefer the multivariate approach is its ability to account for the dependence between multiple estimates from the same study. However, nearly all the existing methods for analyzing multivariate meta‐analytic data require the knowledge of the within‐study correlations, which are usually unavailable in practice. We propose a simple non‐iterative method that can be used for the analysis of multivariate meta‐analysis datasets, that has no convergence problems, and does not require the use of within‐study correlations. Our approach uses standard univariate methods for the marginal effects but also provides valid joint inference for multiple parameters. The proposed method can directly handle missing outcomes under missing completely at random assumption. Simulation studies show that the proposed method provides unbiased estimates, well‐estimated standard errors, and confidence intervals with good coverage probability. Furthermore, the proposed method is found to maintain high relative efficiency compared with conventional multivariate meta‐analyses where the within‐study correlations are known. We illustrate the proposed method through two real meta‐analyses where functions of the estimated effects are of interest. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Longitudinal measurement in health‐related surveys. A Bayesian joint growth model for multivariate ordinal responses

Longitudinal surveys measuring physical or mental health status are a common method to evaluate treatments. Multiple items are administered repeatedly to assess changes in the underlying health status of the patient. Traditional models to analyze the resulting data assume that the characteristics of at least some items are identical over measurement occasions. When this assumption is not met, this can result in ambiguous latent health status estimates. Changes in item characteristics over occasions are allowed in the proposed measurement model, which includes truncated and correlated random effects and a growth model for item parameters. In a joint estimation procedure adopting MCMC methods, both item and latent health status parameters are modeled as longitudinal random effects. Simulation study results show accurate parameter recovery. Data from a randomized clinical trial concerning the treatment of depression by increasing psychological acceptance showed significant item parameter shifts. For some items, the probability of responding in the middle category versus the highest or lowest category increased significantly over time. The resulting latent depression scores decreased more over time for the experimental group than for the control group and the amount of decrease was related to the increase in acceptance level. Copyright © 2012 John Wiley & Sons, Ltd.     

Joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects

We propose a semiparametric joint model for bivariate longitudinal ordinal outcomes and competing risks failure time data. The association between the longitudinal and survival endpoints is captured by latent random effects. This approach generalizes previous joint analysis that considers only one response variable at the longitudinal endpoint. One unique feature of the proposed model is that we relax the commonly used normality assumption for random effects and leave the distribution completely unspecified. We use a modified version of the vertex exchange method in conjunction with an expectation-maximization algorithm to estimate the random effects distribution and model parameters. We show via simulations that robust parameter estimates are obtained from the proposed method under various scenarios. We illustrate the approach using cough severity and frequency data from a scleroderma lung study.     

A joint modeling approach to data with informative cluster size: robustness to the cluster size model

In many biomedical and epidemiological studies, data are often clustered due to longitudinal follow up or repeated sampling. While in some clustered data the cluster size is pre-determined, in others it may be correlated with the outcome of subunits, resulting in informative cluster size. When the cluster size is informative, standard statistical procedures that ignore cluster size may produce biased estimates. One attractive framework for modeling data with informative cluster size is the joint modeling approach in which a common set of random effects are shared by both the outcome and cluster size models. In addition to making distributional assumptions on the shared random effects, the joint modeling approach needs to specify the cluster size model. Questions arise as to whether the joint modeling approach is robust to misspecification of the cluster size model. In this paper, we studied both asymptotic and finite-sample characteristics of the maximum likelihood estimators in joint models when the cluster size model is misspecified. We found that using an incorrect distribution for the cluster size may induce small to moderate biases, while using a misspecified functional form for the shared random parameter in the cluster size model results in nearly unbiased estimation of outcome model parameters. We also found that there is little efficiency loss under this model misspecification. A developmental toxicity study was used to motivate the research and to demonstrate the findings.     

From the Cochrane Library and Diabetes Care: self-monitoring of blood glucose probably an effective way to improve glycaemic control in patients with type 2 diabetes not taking insulin

Self-monitoring of blood glucose has been found to be effective for patients with type I diabetes and for patients with type 2 diabetes taking insulin. There is much debate on the effectiveness of self-monitoring of blood glucose in the management of patients with type 2 diabetes who are not taking insulin. A systematic review of 6 randomised controlled trials comparing self-monitoring of blood glucose with standard care, self-monitoring of urine glucose, or both showed that self-monitoring of blood glucose may be effective in improving glycaemic control in patients with type 2 diabetes who are not using insulin. There was scant data on patient-related outcomes, such as quality of life, well being and satisfaction. Therefore, more large long-term studies of high quality are needed.